A-Math: Solving Indices Equation (Involving Common Base)

This topic is taught in Secondary 3 after introduction of Indices Law.

In solving indices equation involving the same base, one of the common techniques is by Substitution. But before you can do substitution, you need to apply indices law to ‘break down’ the equation. This process of breaking down is sometimes challenging for students. Knowing how to solve quadratic equation is also essential.

Sometimes, solving Indices Equation will also involve the concept of taking lg on both sides as well.

In the following example, you will Substitution and ‘Breaking down’ in action:

Indices-Equation

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9 Responses to A-Math: Solving Indices Equation (Involving Common Base)
  1. engeline
    February 13, 2010 | 12:36 pm

    this is good

    Reply

  2. John kaluba
    February 14, 2010 | 4:35 am

    You are such a great Mathematics. Iam impressed with your method of solving complex equations

    Reply

  3. stephen
    February 14, 2010 | 7:15 pm

    Yes you deserve a big up congratulation.Mathematics is no longer turf subject!

    Reply

  4. j
    February 21, 2010 | 8:25 am

    how would you solve this if ^ means to the power of-
    2^(x)3^(y)=6

    Reply

    j hate Reply:

    with 2 unknowns you need 2 equations to solve for the unknowns

    Reply

  5. lope
    February 2, 2011 | 8:44 pm

    how would you solve this if ^ means to the power of-
    (2^2x+1)9^x=6^x

    Reply

  6. Anon
    April 1, 2011 | 4:47 pm

    wow this is really helpful, thank you soo much!

    can someone help me with this? please

    4^p-3 * 7^q-1 ?

    Reply

  7. lpo
    May 30, 2011 | 7:33 am

    no root exist

    Possible derivation:
    d/dp(4^(p-3) 7^(q-1))
    | Factor out constants:
    = | 7^(q-1) (d/dp(4^(p-3)))
    | Use the chain rule, d/dp(4^(p-3)) = ( d4^u)/( du) ( du)/( dp), where u = p-3 and ( d4^u)/( du) = 4^u log(4):
    = | 7^(q-1) (4^(p-3) log(4) (d/dp(p-3)))
    | Differentiate the sum term by term:
    = | 4^(p-3) 7^(q-1) log(4) (d/dp(p)+d/dp(-3))
    | The derivative of -3 is zero:
    = | 4^(p-3) 7^(q-1) log(4) (d/dp(p)+0)
    | The derivative of p is 1:
    = | 1 4^(p-3) 7^(q-1) log(4)

    Reply

  8. alake
    October 4, 2011 | 5:39 am

    x5=125*squreroot of 2 pls solve d equation

    Reply

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